Convergence to self-similar solutions for a semilinear parabolic equation

Marek Fila; Michael Winkler; Eiji Yanagida

doi:10.3934/dcds.2008.21.703

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2008, Volume 21, Issue 3: 703-716. Doi: 10.3934/dcds.2008.21.703

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Convergence to self-similar solutions for a semilinear parabolic equation

1.
Department of Applied Mathematics and Statistics, Comenius University, 842 48 Bratislava
2.
Department of Mathematics I, Wüllnerstr. 5-7, RWTH Aachen, 52056 Aachen
3.
Mathematical Institute, Tohoku University, Sendai 980-8578

Received: April 30, 2007

Revised: January 31, 2008

Published: August 2008

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Abstract

We study the behavior of solutions of the Cauchy problem for a parabolic equation with power nonlinearity. Our concern is the rate of convergence of solutions to forward self-similar solutions. We determine the exact rate of convergence which turns out to depend on the spatial decay rate of initial data.

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Mathematics Subject Classification: Primary: 35K15, 35K57; Secondary: 35B40.

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